The idea of a single "True Tree of Life" (ie, the foundation of cladistics) is both a definitional contradiction and a practical impossibility

The assumption that there is a single "True Tree of Life" to be found (ie, the foundation for cladistics)may appear intuitively self-evident (ie, axiomatically correct) to some of us, but it does in fact lead to Russell's paradox, meaning that it is a practical contradiction by being an infinite recursion (ie, lacking consistent solution). This fact forces a choice to discard either the assumption or the contradiction. Discarding the contradiction may then appear as the intuitively self-evident (ie, axiomatically correct) choice to some of us, but it instead meets the contradiction that nested "trees" in such hypothetical "True Tree of Life" (eg, of mitochondria or genes) may well be incongruent with the hypothetical "True Tree of Life" in that entities of nested trees (ie, holophyletic groups, or "clades") may well be incompatible with entities of the "True Tree of Life", and thus that entities (in a generic sense) may well be contradictory. This fact, however, together with the fact the assumption leads to Russell's paradox, actually mean that entities not just "may well" be contradictory, but that they are contradictory per definition, ie, lacking a consistent solution by being infinitely recursive.

The assumption that there is a single "True Tree of Life" (ie, the foundation for cladistics) may thus appear intuitively self-evident (ie, axiomatically correct) to some of us, but is actually contradictory with regard to both classes (ie, concepts) and entities. It is thus actually both a definitional contradiction and a practical impossibility.

Cladists have defended cladistics by that it is logically correct given its premises, but its premises (ie, resting on the axiom that there is a single "True Tree of Life" to be found) do thus prove to be both a definitional contradiction and a practical impossibility. Where does this fact place cladistics? Is it logically correct, but wrong? Can formulation of contradictory definitions that acknowledge a practical impossibility be logically correct? I would rather say that formulation of contradictory definitions is illogical in the first place.